We simulate aquifer‐scale reactive transport using an approach based on travel times and relative reactivity. The latter quantifies the intensity of the chemical reaction relative to a reference reaction rate with identical concentrations and can be interpreted as the strength of electron‐donor (or electron‐acceptor) release by the matrix, scaled by a reference release. In general, the relative reactivity is a spatially variable property reflecting the geology of the formation. In the proposed approach, we track the path of individual water parcels through the aquifer and evaluate the age of the water parcels and the relative reactivity integrated along their trajectories. By switching from spatial discretization to cumulative relative reactivity, advective‐reactive transport can be simulated by solving a single system of ordinary differential equations for each combination of concentrations in the inflow. We test the validity of the approach in a two‐dimensional test case of steady state groundwater flow and reactive transport involving aerobic respiration and denitrification. Here we compare steady state concentration distributions of the spatially explicit virtual truth, accounting for dispersive mixing, with the approximation based on cumulative relative reactivity and show that the errors introduced by neglecting dispersive mixing are minor if the target quantities are the mass fluxes crossing a control plane or being collected by a well. We further demonstrate the efficiency of the approach in a synthetic three‐dimensional case study. The proposed approach is computationally so efficient that ensemble runs to assess statistical distributions of concentration time series of reactive solutes become feasible, which is not practical with a spatially explicit model.

Many groundwater contaminants react with components of the aquifer matrix, causing a depletion of the aquifer's reactivity with time. We discuss conceptual simplifications of reactive transport that allow the implementation of a decreasing reaction potential in reactive‐transport simulations in chemically and hydraulically heterogeneous aquifers without relying on a fully explicit description. We replace spatial coordinates by travel‐times and use the concept of relative reactivity, which represents the reaction‐partner supply from the matrix relative to a reference. Microorganisms facilitating the reactions are not explicitly modeled. Solute mixing is neglected. Streamlines, obtained by particle tracking, are discretized in travel‐time increments with variable content of reaction partners in the matrix. As exemplary reactive system, we consider aerobic respiration and denitrification with simplified reaction equations: Dissolved oxygen undergoes conditional zero‐order decay, nitrate follows first‐order decay, which is inhibited in the presence of dissolved oxygen. Both reactions deplete the bioavailable organic carbon of the matrix, which in turn determines the relative reactivity. These simplifications reduce the computational effort, facilitating stochastic simulations of reactive transport on the aquifer scale. In a one‐dimensional test case with a more detailed description of the reactions, we derive a potential relationship between the bioavailable organic‐carbon content and the relative reactivity. In a three‐dimensional steady‐state test case, we use the simplified model to calculate the decreasing denitrification potential of an artificial aquifer over 200 years in an ensemble of 200 members. We demonstrate that the uncertainty in predicting the nitrate breakthrough in a heterogeneous aquifer decreases with increasing scale of observation.

Groundwater abstraction wells are commonly protected by zones of restricted land use. Such well protection areas typically cannot cover the entire well catchment, and numerous risk sources remain. Each risk source could release contaminants at any time, affect the well earlier or later, and thus put the quality of supplied water at risk. In this context, it seems fortunate that most well catchments are equipped with monitoring networks. Such networks, however, often grew historically while following diverse purposes that changed with time. Thus, they are often inadequate (or at least suboptimal) as reliable risk control mechanism. We propose to optimize existing or new monitoring networks in a multi-objective setting. The different objectives are minimal costs, maximal reliability in detecting recent or future contaminant spills, and early detection. In a synthetic application scenario, we show that (1) these goals are in fact competing, and a multi-objective analysis is suitable, (2) the optimization should be made robust against predictive uncertainty through scenariobased or Monte Carlo uncertainty analysis, (3) classifying the risk sources (e.g., as severe, medium, almost tolerable) is useful to prioritize the monitoring needs and thus to obtain better compromise solutions under budgetary constraints, and (4) one can defend the well against risk sources at unknown locations through an adequate model for the residual risk. Overall, the concept brings insight into the costs of reliability, the costs of early warning, the costs of uncertainty, and into the trade-off between covering only severe risks versus the luxury situation of controlling almost tolerable risks as well.

Groundwater wells are often protected by restricted land use within wellhead protection zones. Unfortunately, one cannot restrict land use in the entire catchment (especially in urban areas), and there is uncertainty in wellhead delineation. Thus, nearly all well catchments have an entire inventory of risk sources. Each of these risk sources may fail at any time, release contamination and affect the well earlier or later. In fact, most catchments are equipped with some form of monitoring network. Such networks, however, often grow historically, follow various purposes that changed over time, and thus are often suboptimal (if not even inadequate) for rigorous risk control. In this work, we propose a concept to plan monitoring networks through multi-objective optimization. The different objectives are minimal costs, maximal probability to detect all possible contaminants once they entered the aquifer, and earliest possible detection. Also, risk sources that are classified as severe versus medium or tolerable should be treated with different priorities. Therefore, we propose to treat detection probability and early-warning time as separate objectives for each risk class. The concept will allow catchment managers to obtain optimal monitoring networks for risk control, and to gain insight into the costs of certainty, the costs of early warning, and the costs of covering top risks versus the luxury situation of controlling even minor risks.

Numerical models for reactive transport can be used to estimate the breakthrough of a contaminant in a pumping well or at other receptors. However, as natural aquifers are highly heterogeneous with unknown spatial details, reactive transport predictions on the aquifer scale require a stochastic framework for uncertainty analysis. The high computational demand of spatially explicit reactive‐transport models hampers such analysis, thus motivating the search for simplified estimation tools. We suggest performing an electron balance between the reactants in the infiltrating solution and in the aquifer matrix to obtain the hypothetical time of dissolved‐reactant breakthrough at a receptor if the reaction with the matrix was instantaneous. This time we denote as the advective breakthrough time for instantaneous reaction (τinst). It depends on the amount of the reaction partner present in the matrix, the mass flux of the dissolved reactant, and the stoichiometry. While the shape of the reactive‐species breakthrough curve depends on various kinetic parameters, the overall timing scales with τinst. We calculate the latter by particle tracking. The effort of computing τinst is so low that stochastic calculations become feasible. We apply the concept to a two‐dimensional test case of aerobic respiration and denitrification. A detailed spatially explicit reactive‐transport model includes microbial dynamics. Scaling the time of local breakthrough curves observed at individual points by τinst decreased the variability of electron‐donor breakthrough curves significantly. We conclude that the advective breakthrough time for instantaneous reaction is efficient in estimating the time over which an aquifer retains its degradation potential.

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